The private equity group, which is working with two major Betfair shareholders — Richard Koch and Antony Ball — is understood to have sounded out investors over a revised approach ahead of a takeover panel deadline at 5pm on Monday.

It is believed the new offer, which would value the company close to £1bn, could be tabled to Betfair’s board as early as Sunday. But sources this weekend stressed that conversations were still ongoing and that a final decision had not been made.

One top-10 shareholder suggested on Saturday night CVC may tell Betfair it is not prepared to dramatically raise its offer unless it is allowed access to the company’s books.

Betfair’s board, led by City veteran Gerald Corbett, the former Railtrack chief and chairman of Woolworths, could, in theory, give the consortium access to its books without recommending an offer. The company, which was founded in 2000 by one-time professional gambler Andrew Black and former JP Morgan trader Edward Wray, both still major shareholders, last month rejected CVC’s £912m preliminary offer, saying it “fundamentally undervalues the company and its attractive prospects”.

Betfair’s chief executive, Breon Corcoran, used a trading update last Tuesday to set out the firm’s defence, which included increasing expected cost savings from £20m to £30m and raising full-year revenue forecasts to £387m, up from previous guidance of £370m-£385m.

Mr Corcoran, who joined last summer from Paddy Power, admitted the CVC bid had forced the betting exchange to show “a bit more leg than we might have liked to”, as he seeks to turn the business around.

The group has axed around 500 staff and has withdrawn from markets such as Cyprus, Germany and Greece, where there is unstable online betting regulation.

Ivor Jones, analyst at Numis Securities, raised his target price to £11 a share, from £10, following Tuesday’s presentation. He said the group’s share price was “reasonably well insulated from the disappointment of a bid not emerging”.

A number of institutional investors are understood to have built up stakes in Betfair last week — suggesting the market believes a takeover bid may not come off. CVC, which has been talking to shareholders since Tuesday’s update, declined to comment.

It is understood the private equity group was taken by surprise when news it was in talks over a potential bid leaked out last month. The consortium has the option of asking the Takeover Panel for an extension to the deadline.

Key to any potential deal will be Mr Wray and Mr Black, who between them still hold about 19pc of the shares. Last month Mr Wray backed the board’s rejection of CVC’s bid and expressed support for the group’s new chief executive, saying: “I think Breon is doing a good job.”

Mr Koch is one of Betfair’s early backers and a former management consultant. He has a 6pc stake, despite selling almost a quarter of his shares in 2004 to Japan’s Softbank, a deal that made him £27m before tax. Mr Ball is a non-executive director at Luxembourg-listed investment group Brait.

Betfair’s exchange allows customers to bet against one another, while the group takes a commission.